The Joy of Why

How Can Some Infinities Be Bigger Than Others?

Apr 19, 2023

46:11

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Episode notes

Introduction

2min

The Physics of Infinity

3min

The Importance of Infinity

2min

The Concept of Sets

2min

The Importance of Foundations in Set Theory

2min

The History of Mathematics

2min

The Use of Infinity in Mathematical Calculus

2min

The Countable Integers

2min

The Uncountable Set of Decimal Numbers

2min

10.

The Continuum Hypothesis

2min

11.

The Problem With Counter Examples

2min

12.

The Incomplete Axism in Mathematics

2min

13.

Axioms in Mathematics

2min

14.

The ZFC Axiom of Choice

3min

15.

The Importance of Forcing in Set Theory

3min

16.

The Non-Platonic View of the Real Numbers

2min

17.

The Consensus View on the Continuum Hypothesis

2min

18.

The Importance of Choice in Mathematics

5min

19.

The Continuum Hypothesis and the Axiom of Choice

3min

20.

The Importance of Set Theory

2min

21.

The Joy of Why

2min

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

The post How Can Some Infinities Be Bigger Than Others? first appeared on Quanta Magazine

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